Y. Wei, C.L. Chow¹, C.T. Liu²

CMES-Computer Modeling in Engineering & Sciences, Vol.1, No.4, pp. 71-78, 2000, DOI:10.3970/cmes.2000.001.523

Abstract The paper presents a numerical simulation for mixed mode crack initiation based on the concepts of damage mechanics. A model with two scalar damage variables is introduced for characterization of damage in a material element. Then a tangent modulus tensor is derived for damage-coupled constitutive equations. A failure criterion is developed with the concept of damage accumulation not only to identify the location of damaged element where the crack initiation angle but also to determine the critical load for mixed mode fracture. The damage model developed is incorporated in a general-purpose finite element program ABAQUA through its UMAT subroutine. The… More >

Farid F. Abraham¹

CMES-Computer Modeling in Engineering & Sciences, Vol.1, No.4, pp. 63-70, 2000, DOI:10.3970/cmes.2000.001.515

Abstract A challenging paradigm in the computational sciences is the coupling of the continuum, the atomistic and the quantum descriptions of matter for a unified dynamic treatment of a single physical problem. We described the achievement of such a goal. We have spanned the length scales in a concerted simulation comprising the finite-element method, classical molecular dynamics, quantum tight-binding dynamics and seamless bridges between these different physical descriptions. We illustrate and validate the methodology for crack propagation in silicon. More >

Z. Chen¹, W. Hu¹, E.P. Chen²

CMES-Computer Modeling in Engineering & Sciences, Vol.1, No.4, pp. 57-62, 2000, DOI:10.3970/cmes.2000.001.509

Abstract To simulate the dynamic failure evolution without using nonlocal terms in the strain-stress space, a damage diffusion equation is formulated with the use of a combined damage/plasticity model that was primarily applied to the case of rock fragmentation. A vectorized model solver is developed for large-scale simulation. Two-dimensional sample problems are considered to illustrate the features of the proposed solution procedure. It appears that the proposed approach is effective in simulating the evolution of localization, with parallel computing, in a single computational domain involving different lower-order governing differential equations. More >

Changyu Hwang¹, Philippe H. Geubelle²

CMES-Computer Modeling in Engineering & Sciences, Vol.1, No.4, pp. 45-56, 2000, DOI:10.3970/cmes.2000.001.497

Abstract This paper presents the formulation and numerical implementation of a spectral scheme specially developed to simulate dynamic fracture events in unidirectional and cross-ply fiber-reinforced composites. The formulation is based on the spectral representation of the transversely isotropic elastodynamic relations between the traction stresses along the fracture plane and the resulting displacements. Example problems involving stationary or dynamically propagating cracks in fiber-reinforced composites are investigated and compared with reference solutions available in the literature and/or experimental observations. More >

M. Kögl, L. Gaul²

CMES-Computer Modeling in Engineering & Sciences, Vol.1, No.4, pp. 27-44, 2000, DOI:10.3970/cmes.2000.001.479

Abstract A Boundary Element formulation is presented for the solution of three-dimensional problems of anisotropic elastodynamics. Due to the complexity of the dynamic fundamental solutions for anisotropic materials and the resulting high computational costs, the approach at hand uses the fundamental solution of the static operator. This leads to a domain integral in the representation formula which contains the inertia term. The domain integral can be transformed to the boundary using the Dual Reciprocity Method. This results in a system of ordinary differential equations in time with time-independent matrices. Several general questions concerning the anisotropic solutions, the use of DRM, and… More >

L. Ma¹, A.S. Kobayashi², S. N. Atluri³, P.W. Tan⁴

CMES-Computer Modeling in Engineering & Sciences, Vol.1, No.4, pp. 19-26, 2000, DOI:10.3970/cmes.2000.001.471

Abstract Experimentally determined T_ε^* and CTOA resistance curves were used to simulate numerically, stable crack growth and the ensuing crack linkup in 0.8 mm thick 2024-T3 aluminum tension specimen with multiple site damage (MSD) subjected to monotonically/cyclically increasing loading. The T_ε^* integral correctly predicted the crack growth and linkup history as well as the onset of rapid fracture in MSD specimens. The CTOA criterion also predicted the crack growth history but in its present form, could not predict crack linkup and rapid fracture. More >

A. P. Chassiakos, C. I. Samaras, D. D. Theodorakopoulos¹

CMES-Computer Modeling in Engineering & Sciences, Vol.1, No.4, pp. 9-18, 2000, DOI:10.3970/cmes.2000.001.461

Abstract Time and cost to complete a project is an important tradeoff problem in project planning and control. Existing methods have not provided an accepted solution in terms of both accuracy and efficiency. In an attempt to improve the solution process, a method is presented for developing optimal project time-cost curves based on CPM analysis. Using activity succession information, project paths are developed and duration is calculated. Following that, duration is reduced in an optimal way employing integer programming. Two alternative formulations are proposed which lead to corresponding algorithms, a progressive duration reduction and a direct reduction to the desired level.… More >

J. Sladek¹, V. Sladek¹, V. Kompis², R. Van Keer³

CMES-Computer Modeling in Engineering & Sciences, Vol.1, No.4, pp. 1-8, 2000, DOI:10.3970/cmes.2000.001.453

Abstract This paper presents an application of a direct Trefftz method with domain decomposition to the two-dimensional elasticity problem. Trefftz functions are substituted into Betti's reciprocity theorem to derive the boundary integral equations for each subdomain. The values of displacements and tractions on subdomain interfaces are tailored by continuity and equilibrium conditions, respectively. Since Trefftz functions are regular, much less requirements are put on numerical integration than in the traditional boundary integral method. Then, the method can be utilized to analyse also very narrow domains. Linear elements are used for modelling of the boundary geometry and approximation of boundary quantities. Numerical… More >

José A. González, Ramón Abascal¹

CMES-Computer Modeling in Engineering & Sciences, Vol.1, No.3, pp. 141-150, 2000, DOI:10.3970/cmes.2000.001.443

Abstract In this work an approach to the two-dimensional steady-state rolling contact problem, with and without force transmission, is presented. The problem is solved by the combination of the Boundary Element Method with a formulation of the variational inequalities that govern the problem in the contact area, producing finally a mathematical programming problem. This formulation avoids the direct use of the contact constrains, but it drives to the minimisation of a non-differentiable function, being necessary the use of an specific numerical tool as the modified Newton's method. More >

S. Guimarães¹, J.C.F. Telles²

CMES-Computer Modeling in Engineering & Sciences, Vol.1, No.3, pp. 131-139, 2000, DOI:10.3970/cmes.2000.001.433

Abstract The paper discusses further applications of the hyper-singular boundary integral equation to obtain the Green's function solution to general geometry fracture mechanics problems, such as curved multifracture crack simulation, static and transient dynamic in 2-D, 3-D and plate bending problems. This numerical Green's function (NGF) is implemented into alternative boundary element computer programs, as the fundamental solution, to enhance the scope of alternative applications of the NGF procedure.
The results to some typical linear fracture mechanics problems are presented. More >